We've had a virus within the company recently that used Acrobat Reader as it's infection route.
What would people's recommendations be for a secure PDF viewer? Ideally as fully featured as possible.
I've found PDFXchange to be a better Windows citizen than Foxit. 64-bit client, preview handler, doesn't use a weird shortcut, better at running non-admin, etc. Back when I ran Foxit, I'd keep running into little irritants that required workarounds.
Foxit is available cross-platform; PDFXchange is Windows-only. Coincidence?
You can check SumatraPDF. It's minimalistic. Light, fast and virus-proof.
Now fully-featured and secure... I guess not running on Windows, and switching OS is probably too much cost for a company.
Google Chrome now has built-in PDF viewer, based on the Foxit PDF SDK. The PDF viewer in Chrome runs within a sandbox, making it difficult for malicious software to escape. If your organization uses Chrome, then you should be able to use that for viewing most PDF documents. You asked for a "fully featured" application, which this is not really, so (as suggested in other answers) you can also use the full Foxit PDF reader application when you need more tools, but honestly the features in the Chrome viewer should be sufficient for viewing files, and will likely be the safest method.